Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.map_map

∀ {L : FirstOrder.Language} {M : Type w} {N : Type u_1} {P : Type u_2} [inst : L.Structure M] [inst_1 : L.Structure N]
  [inst_2 : L.Structure P] (S : L.Substructure M) (g : L.Hom N P) (f : L.Hom M N),
  FirstOrder.Language.Substructure.map g (FirstOrder.Language.Substructure.map f S) =
    FirstOrder.Language.Substructure.map (g.comp f) S

Defined in

Mathlib.ModelTheory.Substructures

Cited by

1 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FirstOrder.Language.StructureFirstOrder.Language.StructureFirstOrder.Language.Structure